PPT-Heat-conduction/Diffusion Equation

Douglas Wilhelm Harder MMath LEL Department of Electrical and Computer Engineering University of Waterloo Waterloo Ontario Canada eceuwaterlooca dwharderalumniuwaterlooca 2012 by Douglas Wilhelm Harder Some rights reserved. Governing Equation:. Dirichlet Boundary Conditions:. Solution:. Heat Flux:. Heat Flow:. temperature . is not . a function of . k. Notes:. . A. is the cross-sectional area of the wall . perpendicular. 3.1 …………. Introduction. 3.2 …………. Biot and Fourier Number. 3.3 …………. . Lumped heat capacity analysis. 3.4 …………. Time constant and response of a thermocouple. 3.5 …………. Transient. of Change II. 7. Heat Equations of Change. . 7.1. Derivation of Basic Equations. . 7.1.1. Differential Equation for Heat Conduction. . 7.1.2. Energy Equation. . 7.1.3. . Advisor: Professor Anna . Mazzucato. Graduate Student: . Yajie. Zhang. Solving a Transmission Problem for the 1D Diffusion Equation. Transmission Problem for the 1D Heat Equation. Diffusion coefficient c jumps at x=1/2 (the interface). Impose transmission conditions at interface. Solve equation in [0,1]. Impose . Fins. extended surfaces that enhance fluid heat transfer to/from a surface in large part by increasing the . effective surface area . of the body. combine . conduction through the fin. and . convection to/from the fin. The process which heat or electricity is . directly. transferred through a substance when there is a difference in temperature or electrical potential. . Conduction = TOUCHING . Conduction. Convection. Conduction problems may involve multiple directions and time-dependent conditions. Inherently complex – Difficult to determine temperature distributions. One-dimensional. . steady-state. models can represent accurately numerous engineering systems. of Change I. So far…. Outline. Heat Transfer Mechanisms. Conduction Heat Transfer. Convection Heat Transfer. Combined Heat Transfer. Overall Shell Heat Balances. Heat Equations of Change. 6. Heat Equations of Change. . An Educational Presentation. Presented By:. Joseph Ash. Jordan Baldwin. Justin Hirt. Andrea Lance. History of Heat Conduction. Jean Baptiste Biot. (1774-1862). French Physicist. Worked on analysis of heat conduction. Advisor: Professor Anna . Mazzucato. Graduate Student: . Yajie. Zhang. Solving a Transmission Problem for the 1D Diffusion Equation. Transmission Problem for the 1D Heat Equation. Diffusion coefficient c jumps at x=1/2 (the interface). Impose transmission conditions at interface. Solve equation in [0,1]. Impose . ComputersConduction cooling for modular embedded computers have been used for many years in applications where air cooling is not appropriate Standardization efforts in that domain have early helped t conductionXiaoshan XuThe importance of thermal conductioneEnergy consumptionetransfer through conductioneEnergy generationeThermoelectric effect Seebeckeffect eSpin SeebeckeffectHot reservoirCold rese George Green. George Green. (14 July 1793 – 31 May 1841) was a British mathematical physicist who . wrote: . An . Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. Shape Evolution of Heat Exchanging Surfaces… . P M V Subbarao. Professor. Mechanical Engineering Department. Forced Convection Cooling of Chips Using Air. Analytical Convective Heat Transfer. 1701 Newton’s law of cooling..